Crossing indices, traits and the principle of indistinguishability

Igor Nikonov

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arXiv · 2110.14218

Crossing indices, traits and the principle of indistinguishability

Igor Nikonov

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Abstract

A (weak chord) index is a function on the crossings of knot diagrams such that: 1) the index of a crossing does not change under Reidemeister moves; 2) crossings which can be paired by a second Reidemeister move have the same index. We show that one can omit the second condition in the case of the universal index. As a consequence, we get the following principle of indistinguishability for classical knots: crossings of the same sign in a classical knot diagram can not be distinguished by any inherent property.

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Igor Nikonov. 2021-10-27. Crossing indices, traits and the principle of indistinguishability. https://arxiv.org/abs/2110.14218

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